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\begin{document}
\frontmatter
\textbf{{\Huge Quark Gluon Plasmas}}
\begin{wrapfigure}{r}{0.20\textwidth}
\centering
\includegraphics[width=0.15\textwidth]{gnolldruid1.eps}
\caption{a plasma scientist}
\end{wrapfigure}

\mainmatter
\chapter{\large Introduction}

parton = gluons and quarks
partons have spin

\chapter{\large Plasma Forces and Baryonic Matter}


Electric potential is the manifold form of Debye length. Debye length is a measure of how mobile charge
carriers screen out electric fields. Plasma consists of ionic gas. Quark Gluon Plasma is also due to
very high temperatures. It is a plasma which reaches another critical temperature to change the ions
into quarks and their Goldstone bosonics e.g. gluons. Goldstone bosons are massless exchange particles.
They exist purely to change forces, energy or matter into their counterparts. 
To exchange quarks into other quarks or to change their spins the gluons use transmission of color forces.
Gluons exert color force as a the strong force. The color force is described in chapter 3 as the theory
of Quantum Chromo Dynamics (chromos = color.) In this chapter we will look at an example of the forces
without quarks but at an upper level : the van der Waals and electric force. Maxwell's law (4th)
describes the photoelectric field as a Lagrangian. This will be shown in a few steps.

\section*{\large Hadron Heavy Ion Collider}

The best known hadrons are the proton and the neutron. In CERN's LHC (Large Hadron Collider) scientists 
seek for the answer of existence of the big bang's precursor state of matter. The state of an extraordinary 
plasma, QGP (Quark Gluon Plasma.)
\\
My contribution to this are some calculations and a formula compendium
to describe this 5th form of matter the first 5 being solid,liquid,gas
and plasma.
\\
Where ordinary plasma is concerned it depends on ions (negative and positive.)
\\
The QGP contains broken down plasma which is a quark and gluon composition. There is 
however no evidence in the fact that gravitons would not co-exist in it.
\section*{\large electrons screening out electric fields}
The potential energy of charge $q_{j}$ is given by $U(x)$ :
$U(x) = -\bigtriangledown{\Phi(x)}\\$

The change in potential is given by 

$\bigtriangledown^2{\Phi(x)} = \frac{1}{\epsilon_{r}\epsilon_{0}} \Sigma{q_{j}n_{j}(r)}\\$
with the concentration of charge $q_{j}\\$  
$n_{j}(r) = n_{j}^{0} e^{\frac{q_{j}\Phi(x)}{k_{B}T}}\\$ with $n_{j}^{0}$ the mean concentration of charge j.
The Poisson-Boltzmann concentration :
$\bigtriangledown^2{\Phi(x)} = \frac{1}{\epsilon_{r}\epsilon_{0}} \Sigma{q_{j}
n_{j}^{0} e^{\frac{q_{j}\Phi(x)}{k_{B}T}}}\\$
The spherical field of potential $U(x,y,zi,q)$ is 
$-\int_{x}{\int_{y}{\int_{z}{\bigtriangledown^2\Phi(x,y,z,q)}}}$
However this only works for $\frac{\phi}{{q_{j}}}$ as the charge carrier without 
a charge distribution, as a point charge.\\
There exists a manifold which depends on the changing charge at different
poistions 
$-\int_{x}{\int_{y}{\int_{z}\int_{q}{\bigtriangledown^2\Phi(x,y,z,q)}}}$
With charge conservation q becomes constant or charges can change over time. 
\\
The formula can have a time-dpendent integral if the charge distributions
together with their densities and position/velocity define the time functor.
Note that the coordinates of the densities i.e. the poistions can be 
variant under the Galilean transformations in a time-variant QGP. 
\\
The main formula then becomes 
$-\int_{x}{\int_{y}{\int_{z}\int_{q}\int_{t}{\bigtriangledown^2\Phi(x,y,z,q)}}}$
\\The time function is only in the conservation of charge as electric fields
influence each other e.g. by changing the charge carrirer's position.	
\\
The Taylor expansion of the exponential term we get the Debye-Huckel equation  
$e^{\frac{q_{j}\Phi(r)}{k_{B}T}} = 1 - \frac{q_{j}\Phi(r)}{k_{B}T}$
\\
The Debye length is the inverse of the quadratic first part of the above equation
and yields the discrete Debye length\\
$\lambda_{D} = \sqrt{\frac{\epsilon_{0}\epsilon_{r}k_{B}T}{\Sigma_{j}^Nn_{j=1}^0q_{j}^2}}$
\\
In a plasma the Debye length is
$\lambda_{D} = \sqrt{\frac{\frac{\epsilon_{0}k_{B}}{q_{e}^2}}{\frac{n_{e}}{T_{e}}+\Sigma_{ij}\frac{j^2n_{ij} }{T_{i}}}}$
\\
This formula takes charges from electrons coupled with an electric field interaction length.
\\
Instead of the time dependency there should also be a color dependency or quark charm dependency.

The Dirac field equation probably is a general case of our take 5 integral but without the
time and charge variance.
The Dirac field equation is\\
$\psi(x) = \frac{d^3p}{(2\pi)^3} \frac{1}{\sqrt{2E_{p}}} \Sigma_{s}(a^spu^s(p)e^{-ipx} + b^spv^s(p)e^{ipx})$
\\
Which means that the Debye length potential energy field equations are the same for fermions instead of hadrons 
with the fact that both exponentials (of e) are summed and can be complex numbers. Thus the
Dirac field equations are a general case of Debye fields (screening length potential energy fields.) 
the logical part about this is that bosons such as the electron have spin 0 and thus yield
much simpler equations than for other particles such as fermion-Goldstone-bosons.
Note that QGP depend on time and that fermions also depend on time which gives another
explanation to Lorentz/Galilean transformation invariance of a photon where in the 
QGP a hadron is baryonic matter and thus depends on time equations.
Also bosons can travel backwards in time with negative energies and our QGP
also allows it because the time depedent functor can be negtive (or complex and negative.)
The complexity of the exponentials come together when they are both substracted e.g.
$e^{ipx}$ and $e^{-ipx}$ both have symmetry in their probabalitities where $e^X$ can never be zero.
So for an electron the probability is never zero. It can however be infinity if T = 0.
The strong force between neutron and proton hadrons shields (Debye length) or lenses (as cosmological lensing)
with quarks due to color and charm.
\\
The van der Waals attraction in energy form for a molecule on distance D is\\
$w(r) = -2 \pi C_{\rho_{1}}\int_{D}^{\infty}\int_{x=0}^{\infty}\frac{xdx}{(z^2+x^2)^3}$
which gives\\
$w(r) = \frac{2\pi C\rho_{1}}{4}\int_{D}^{\infty}\frac{dz}{z^4}$
and\\
$w(r) = -\frac{\pi C\rho_{1}}{6D^3}$
\\
with z = 0 where the molecule is and z = D where the surface is. $\rho_{1}$ is the number density.
\\
Concluding part 1 of this thesis is to take molecules consisting of ions for example inside the
QGP and so we get the van der Waals - electric shielding equation:\\
$e(x) = w(r) + \int_{t}\bigtriangledown \Phi(r) - q_{j} \bigtriangledown \Phi(r)$
\\
The third term is the coulomb force.
\\
Note that there is again a substraction. This is a Lagrangian density function which
is applied on electric force and electric potential inside a QGP.\\
Thus $L = E_{kinetic} - E_{potential}$ and
$\frac{d}{dt}\frac{\delta \zeta}{\delta \phi'} = \frac{\delta \zeta}{\delta \phi}$\\
\\
\begin{figure}[h!]
\caption{$\alpha e^{-ipx} - \beta e^{ipx}$}
\includegraphics{stairwaytoheaven.eps} 
\end{figure}


\chapter{Gluons}
\begin{wrapfigure}{r}{0.30\textwidth}
\centering
\includegraphics[width=0.25\textwidth]{splinter.eps}
\caption{Master Splinter}
\end{wrapfigure}
In the previous chapter we saw that the strong force glues quarks together and that quark color
also plays a role in baryonic matter. The strong force between nucleons in fact is the color
combination of the quarks which act such that the nucleus is held together.\\
The nucleus is only active as a force when there is radioactive radiation. In a "pure" QGP 
there is no bond between quarks to keep them together. Thus a QGP is radioactive.\\
The other way round the gluons are the Goldstone bosons for color force to keep their upper counterpart
together. There are 3 quarks inside a baryon and one up-quark and one down-quark in a meson.

\section*{Color charm}

When a quark strong bond breaks the quark emits its color. This is why radioactiveness is mentioned
to be green radiation. As you can tell there is radioactive radiation in several colors.
Note that hadrons are composed of baryons and mesons.
Quarks also have charm : up, down and strange : u,d, s. Color or isospin in quarks is the charm
categorisation of quarks. u and d quarks have similar masses and a proton for example as a hadron
has an up down and strange quark.  A meson has one up and one down quark. Theories of penta-quarks
exist as the ring of 5 quarks can be made due to their charm. The strong force combination works.
\\
It is believed that quarks are confined. There are no free quarks around except theoretically in
our  Quark Gluon Plasma . With high energy (or temperature) the strong force is known to be very weak.
The interaction between gluons and quarks may even cease to exist but this has not yet been proven.
This principle is known as asymptotic freedom.
\section*{Colored plasma}

Quarks have three colors : green, blue and violet. An ordinary plasma has some unusual 
properties. 
\begin{wrapfigure}{r}{0.30\textwidth}
\centering
\includegraphics[width=0.25\textwidth]{plasmalamp.eps}
\caption{Plasma lamp emitting a violet color}
\includegraphics[width=0.25\textwidth]{quarkgluonplasma.eps}
\caption{a colored quark gluon plasma}
\end{wrapfigure}
\begin{itemize}
\item[1]{degree of ionization : $\alpha = \frac{n_{i}i}{n_{i} + n_{a}}$ $n_{i}$ for ion density and $n_{a}$ 
for neutral atom density. Some atoms have lost or gained electrons. See also chapter 2 for electric field shielding}
\item[2]{energy or temperature in MegaelectronVolts or Kelvin. The key formula here is the Maxwell-Boltzmann equation
with spare UV emission. The color of UV is violet for some}
\item[3]{filamentation : a plasma connects contrary particles due to the different charges. There are string-like
structures which are these connectors.}
\item[4]{conductivity : infinite} 
\item[5]{plasma pinch : the electrical breakdown in plasma due to ion dispersion. Lightning is a plasma pinch} 
\item[6]{shocks due to short Debye length (see chapter 2)} 
\item[7]{lasers can create ions or plasma} 
\item[8]{Rydberg matter is a dusty plasma. It is an impure plasma with lattice grids and containing 'dust' (such
as dust in space.) The principal quantum number of Rydberg atoms is very high and also because of a excited state of the atom} 
\item[9]{solar regions or solar spheres (for example the photsphere) consist of plasma due to high temperature/energy and
high density of ions}
\item[10]{plasma is the 4th state of matter} 
\item[11]{plasma color TVs use the color charm of quarks to produce pixels on-screen of different colors (altough with a blue or green hue). }
\item[12]{plasmas can be neutral or non-neutral due to local charge distributions.}
\item[13]{current inside a plasma can be double layered. A semiconductor is also double-layered. It makes electrons
move from one semi-X to another semi-Y, where X is the first part of the semi-conductor and Y is the other part of
the semiconductor. Both parts contain excited atoms which let flow current from X to Y}
\item[14]{ultracold plasmas can be shot at with a laser to create ions. A magneto-optical (MOT) trap creates a cold plasma by
creating the right color of the excitation}
\item[15]{There is lensing due to plasma and dark matter in space which creates a hue of the same color of the
light which generates plus the fact that there is invariance with this in space-time. The Galilean (Lorentz) transformation
does not change light. It is however possible to make light travel through space and bending e.g. with black holes which 
theoretically consist of the dark matter in space not the plasmas. This is a theory for graviton pulls or space-time
curvature due to polarized light sources such as a sun.} 
\item[16]{plasma is not radioactive. It consists of ions and the electromagnetic forces not quarks and Chromodynamics (QCD) due to the strong force} 
\end{itemize}

Debye sheath or electrostatic sheath is a layer inside a plasma which is more positively charged.
The discharges between positive and negative potentials inside a plasma are time-variant i.e.
they ensure that there is a current a magnetic field and electron jumps, the latter with the photo-electric effect
or on orbitals of non-ionic atoms.\\
To possess a color charge is to be able to emit colors. As a QGP is a  state of matter which is even more
energetic the ions disappear and become color charged quarks. See both pictures for a comparison on color emission.
\\
There exists no evidence however that a QGP does not contain any confined matter or other states of matter.
Due to experiments (such as RHIC \cite{rhicpaper}) the QGP should be non-confined but this is only a theory.\\
It is however clear that empirical evidence showed that the violet quark ( or strange quark) is responsible for
the blue color of a plasmalamp.
\\
\section*{The Relativistic Heavy Ion Collider (RHIC)}
The RHIC \cite{rhicpaper} is a machine which makes sure we get to our plasmas of quarks and gluons. It uses
a beam of ions which collide on other ions. An ion is a composition of neutrons, protons and the atom itself.
During collision several anti-particles, pions, kaons come into existence.\\
The trick is not to use any electrons so the quarks inside the neutrons and protons are the only things which
break loose. Thus only quarks and their color exchange particles can exist in a QGP.\\
The RHIC machine uses heavy ions for example gold (Au) ions. Due to the rather large nucleus there is 
high energy involved in ther collision and further splitting into quarks. This is why most collider machines 
are useful in courses of High Energy Physics. For example there is an energy loss of 73GeV\cite{rhicpaper}
where $1 eV = 1.602 * 10^{-19}$ per nucleon during QGP brewing.
In total the energy removed from the beam in an Au + Au collision is 26TeV. The Debye length in a sun is about $10^{-11}m$
In a sun there is also extensive electric shielding together with an electron density $n_{e}$ of $10^{32} m^3$.\\
The experiments showed that energy densities of parton production exceeds that of the hadrons' energy density.\\
 
\section*{Large Hadron Collider (LHC)}
The LHC is located in Switzerland, Geneva and is the largest particle accelerator in the world as of this day of writing.
Matter is heated to temperatures in there to 100 times that of the sun. The cooling is about -273 C which is colder
than outer space.\\
There are other expermiments at CERN which are a result of QGP : The Low Energy Antiproton Ring (LEAR) produces
what is known as an anti-hydrogen antiatom. anti-hydrogen contains a positron and an anti-proton. Clearly a positron
is also called an anti-electron. This is what CERN published as the True Story of anti-matter.\\
A Cathode Ray Tube (CRT) uses the same principle as the LHC. It accellerates ions onto other ions with magnets
in the beam chamber (the tube itself) and then emitting color. Clearly, a CRT is hot to excite electrons onto
the screen.

\begin{SCfigure}%wrapfigure}{l}{0.2\textwidth}
\includegraphics[width=0.5\textwidth]{partondistribution.eps}
\caption{partons : gluon (red) and up (green),down (blue), strange (violet) quark probability distribution}
\end{SCfigure}


\section*{The Quantum Chromodynamical Lagrangian}
The gauge invariant QCD Lagrangian is \\
$\zeta_{QCD} = \psi_{i}^{-}(i\gamma^{\mu}(D_{\mu})_{ij} - m \delta_{ij})\psi_{j} - \frac{1}{4} G_{\mu v}^a G_{a}^{\mu v}$\\
$\zeta_{QCD} = \psi_{i}^{-}(i\gamma^{\mu}\delta_{\mu} - m )\psi_{i} - gG_{\mu}^a\psi_{i}\gamma^{\mu}T_{ij}^a\psi_{j} - \frac{1}{4} G_{\mu v}^a G_{a}^{\mu v}$
\\
with
\begin{itemize}
\item{$\psi_{i}(x)$ the quark field, a dynamical function of space-time}
\item{in the SU(3) gauge group i,j ..., $G_{\mu}^a(x)$ the gluon fields, a dynamical function of space-time}
\item{a ,b , ... $\gamma^\mu$ Dirac matrices connecting the spinor to the vector representation of the Lorentz group}
\item{$T_{ij}^i$ generators connecting fundamental and antifundamental and adjoint representations of the SU(3) group}
\end{itemize}
	
\appendix
\backmatter

\bibliographystyle{plain}
\bibliography{refs} % plasmamath.bib


%article Zhou
%article Savvides 
\end{document}
